Quantum Synchronization of Twin Limit-Cycle Oscillators

Abstract

Quantum synchronization has been a subject of intensive research in the last decade. In this work, we propose a quantum Liénard system whose classical equivalent features two limit cycles to one of which the system will converge. In the quantum case, both limit cycles coexist in a single steady state. Each of these limit cycles localizes to a distinct phase if coupled to an external drive: one quantum state can thus be assigned two phases. Furthermore, coupling two such oscillators leads to the simultaneous appearance of synchronization and a synchronization blockade. To shed light on this apparent paradoxical result, we introduce finer measures of quantum synchronization.

7+7 pages, 3+5 figures; corrected typos, added references, improved Fig. 2, added Section 2 in Supplemental Material with Fig. S2